Redox-based ion-gating reservoir consisting of (104) oriented LiCoO2 film, assisted by physical masking

Reservoir computing (RC) is a machine learning framework suitable for processing time series data, and is a computationally inexpensive and fast learning model. A physical reservoir is a hardware implementation of RC using a physical system, which is expected to become the social infrastructure of a data society that needs to process vast amounts of information. Ion-gating reservoirs (IGR) are compact and suitable for integration with various physical reservoirs, but the prediction accuracy and operating speed of redox-IGRs using WO3 as the channel are not sufficient due to irreversible Li+ trapping in the WO3 matrix during operation. Here, in order to enhance the computation performance of redox-IGRs, we developed a redox-based IGR using a (104) oriented LiCoO2 thin film with high electronic and ionic conductivity as a trap-free channel material. The subject IGR utilizes resistance change that is due to a redox reaction (LiCoO2 ⟺ Li1−xCoO2 + xLi+ + xe−) with the insertion and desertion of Li+. The prediction error in the subject IGR was reduced by 72% and the operation speed was increased by 4 times compared to the previously reported WO3, which changes are due to the nonlinear and reversible electrical response of LiCoO2 and the high dimensionality enhanced by a newly developed physical masking technique. This study has demonstrated the possibility of developing high-performance IGRs by utilizing materials with stronger nonlinearity and by increasing output dimensionality.


LiCoO 2 redox-IGR device structure and electrical characteristics
The general model of RC is shown in Fig. 1a.Time-series data are input to the reservoir to obtain the reservoir state vector 1 .The time series data input to the reservoir is transformed nonlinearly into a high-dimensional feature space as reservoir states X i (i = 1, 2, …, N).In a full-simulation reservoir such as an echo state network, this nonlinear transformation is performed by a complex network with activation functions defined by sigmoid functions, etc., while in a physical reservoir, it is computed directly by the nonlinear dynamics inherent in the physical system 4,[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] .To obtain the desired output, the readout weights w i are trained by a simple algorithm, such as linear regression, and the reservoir output y(k) is obtained by a linear combination of the reservoir state X i (k) and the weights w i as follows: Here, N, k and b are the reservoir size, discrete time step and bias, respectively.A schematic of our LiCoO 2 redox-IGR, implemented for physical reservoir computing, and cross-sectional scanning electron microscopy (SEM) micrograph of a LiCoO 2 redox-IGR, are shown in Fig. 1b.Ti (5 nm)/Pt (35 nm) source and drain electrodes were deposited by electron beam evaporation on the surface of a SrTiO 3 (100) substrate.LiCoO 2 film (100 nm) was deposited by pulsed laser deposition (PLD) using an Nd:YAG laser operating at 266 nm wavelength, with an O 2 gas fixed flow supplied at a rate of 5.4 sccm.The substrate temperature was kept at 600 °C during deposition.Li 3 PO 4 (300 nm) and Si (20 nm) were deposited by the RF sputtering method at room temperature using Li 3 PO 4 and Si targets, respectively, with a supply of pure Ar gas at a fixed flow rate of 10 sccm.Sputtering times were 180 min for Li 3 PO 4 target and 8 min for Si target, respectively.And sputtering power and pressure were 50 W and 0.93 Pa for both Li 3 PO 4 and Si targets.We chose the amorphous Li 3 PO 4 because it owns compatibility with relatively high Li + conductivity and stability.That is the reason why the amorphous Li 3 PO 4 is widely used as a solid electrolyte for solid-state batteries 43,44 .Si was used for the gate electrode, since it is a promising material for the anodes of solid-state lithium batteries due to its high Li capacitance and low working electric potential 29,40 .A Pt current collector (50 nm) was deposited on the Si by electron beam evaporation.Two drain electrodes and a source electrode were fabricated so that the channel lengths were 5 and 20 µm, with a channel width of 500 µm as shown in lower left panel of Fig. 1b.
Figure 1c shows the XRD pattern for a LiCoO 2 thin film on a SrTiO 3 single crystal.The diffraction peak observed at 2 θ of 45.24° is assigned to LiCoO 2 (104) 45 (JCPDS card no.75-0532).Fabricated LiCoO 2 thin film has no impurity phase, since there was no peak originating from other than (104).The lattice spacing calculated from the diffraction peak was 2.00 Å, which is in very good agreement with the bulk value of 2.00 Å 46 .Crosssectional TEM observation of the LiCoO 2 /SrTiO 3 interface shown in Fig. 1d was performed in order to obtain more detailed information on its crystallinity.Electron diffraction of the LiCoO 2 shows that the LiCoO 2 grew in 104 orientations, perpendicular to the substrate surface, which result is the same as for the XRD pattern.Furthermore, clear diffraction spots can be seen for directions parallel to the substrate surface, indicating that the LiCoO 2 thin film has high crystallinity with aligned in-plane orientation.
By using a (104)-oriented Li + -hole mixed conduction LiCoO 2 thin film as a channel, which exhibits high hole and ion conductivity 46 , we investigated the improvement of device operating speed and computational performance through the rapid and smooth insertion and desertion of Li + .By application of a V G , this IGR (1) changes the channel resistance by inserting (deserting) Li + into (from) the channel through the redox reaction shown below as Eq. ( 2): www.nature.com/scientificreports/When a negative V G is applied, Li + are removed from the channel (i.e., x increases) and move through the solid electrolyte to the Si gate electrode shown in the lower panel of Fig. 1b.During the removal of Li + from the channel, Co 3+ is oxidized to Co 4+ and electron holes are generated to maintain charge neutrality.This is accompanied by an increasing in the electrical conductivity of the Li 1−x CoO 2 .This reaction in high quality LiCoO 2 thin film is highly reversible [40][41][42]46 , so when a positive V G is applied, the conductivity of the channel decreases as Li + are inserted into the channel (i.e., x decreases). Tomeasure the resistance modulation of the channel with respect to the V G , we measured the drain current (I D ) during V G sweeping.
The electrical characteristics of the fabricated device were analyzed at room temperature, in a vacuum chamber, using the source measurement unit (SMU) of a semiconductor parameter analyzer (4200A-SCS, Keithley).Materials in our devices were so stable that we could fabricate our devices in air, although we performed electrical measurements in vacuum for keeping our devices in the best condition.Such condition can be easily obtained by using encapsulation technology 47 , which has been well established for fabrication of integrated circuits (ICs) in commercial electronic devices.For example, transfer molding and compression molding using various types of resin (semiconductor encapsulant) are widely used to keep ICs in vacuum to protect them.Therefore, there is no severe limitation to practical applications.The normalized I D -V G curve of the redox-IGR is shown in Fig. 1e.The V G was swept from 0 to − 4.5 V and then back to 0 V at various sweep rates, ranging from 15 (slow) to 200 mV/s (fast).Nonlinearity in I D change was confirmed from the I D by the redox reactions shown in Eq. ( 2).These are associated with the insertion and desertion of Li + that changes the channel resistance, and a clear hysteresis curve can be drawn at any sweep rate, which suggests that the device exhibits short-term memory, which in turn is a necessary function for reservoirs [1][2][3][4][5][6][7] .Generally, a dynamical system with a specific time constant shows a hysteresis when an external stimulation with a time constant, which is close to the one of the dynamical systems, is applied.In contrast, when the input is sufficiently faster than the time constant of the dynamical system, the response does not follow and does not show hysteresis.Also, when the input is sufficiently slow, the response corresponds to the steady state of the system and does not show hysteresis.Therefore, the extent of hysteretic behavior has a peak with respect to the speed of external stimulation.In the present case shown in Fig. 1e, the hysteresis of 20 mV/s is larger than the one of 15 mV/s because the sweep rate of 20 mV/s is closer to the peak discussed above.
Changes in drain and gate currents when a single pulse of gate voltage is applied are shown in the Fig. 1f.Each current relaxation was fitted with Eq. (3) as shown in black dotted lines.
Relaxation time τ was 290 and 630 ms , respectively.(The other fitting parameters and details of the fitting can be found in Supplementary Table S1).The drain and gate currents show a relaxation with respect to the pulse input, indicating that the device has short-term memory.Different drain and gate current relaxation times enhance the diversity of the nodes and improve computational performance.In particular, the gate current has a nonlinear and complex response to the V G pulse, and the complex response is expected to lead to higher computational performance as in EDL-IGRs 25 .Our IGR utilized such nonlinear I D , I G responses to Li + insertion and desertion into LiCoO 2 channel, driven by V G input, as the nonlinear dynamics function that makes it possible for physical reservoirs to perform information processing.
The subject IGR is operated by a V G pulse stream 25,26 .The time-course nonlinear response of I D and the gate current (I G ) outputs are shown in Fig. 1g.The upper panel of the figure shows the V G pulse stream, which is the input from the IGR.The middle panel of the figure shows that different responses were obtained by using the two drain electrodes with different channel lengths.Upon application of the V G pulse stream, the effective potential drops on the two channels are different due to different channel resistance, which is useful to enhance the diversity of the I D response 25 .Since the I G has a different shape and nonlinearity from I D , the I G shown in the lower panel of the figure was also used in the reservoir calculation 26 .The behavior of the I G is different from the I D , and the use of the I G in the calculation is expected to enhance the high dimensionality of the reservoir and to significantly improve its computational performance.
Concerning the relatively slow operation speed, it can contribute to process a time-series data with slow change.In order to process time series data with a specific speed, response speed of the physical reservoir should cover the dynamics of the data.Therefore, in order to process a time-series data with slow change, the physical reservoir with slow response to input signal is needed.A typical example of that is the predication task of blood glucose level with slow change, which exhibits several ups and downs over several hours in a day 48 .

Physical masking, for high dimensionality enhancement, implemented by drain voltage pulses
Masking is a pre-processing of input whereby the dimensionality of a physical reservoir system is effectively maximized 1,49 .In order to achieve high dimensionality, which is one of the characteristics required for reservoirs, the number of outputs (reservoir states) obtained from the reservoir for a given input must greatly exceed the input dimension.In system reservoirs, high dimensionality can be easily achieved by increasing the network size (number of nodes), but it is generally difficult to obtain a sufficient number of reservoir states physically in a physical reservoir due to limitations such as measurement probes 26 .Therefore, the virtual node method, which virtually considers the time evolution of the response to the input obtained from the physical system as spatially distinct nodes, is widely adopted in physical reservoirs.However, it is difficult to achieve sufficiently high dimensionality by simply using the transient responses of the physical system as different nodes in RC, because neighboring virtual nodes behave in a similar manner, and the effective number of nodes does not increase.
(2) www.nature.com/scientificreports/Thus, by combining the input signal with a masked waveform containing fluctuations (masking), the virtual nodes behave differently from each other and high dimensionality can be improved.Masking is performed by introducing a (N M × Q) mask matrix M for the Q-dimensional input signal u(k), as follows: Here, N M and J(k) are the number of mask dimensions and the masked input signal, respectively; M is always fixed at times k, and a random number sequence or random bit sequence is used.For example, the masked input J(k) is an N M -dimensional vector if Q = 1.When J(k) is actually input to the physical system, these N M elements are input to the physical system at a fixed time interval θ.Then, after completing input of the N M masked input signals (i.e., after θ × N M has elapsed in real time t), the next step of input J(k + 1) is performed in the same manner.In this way, masked input is generated by synthesizing raw input with a specific mask waveform, including random ones, as a pre-processing of the input signal.By designing the mask matrix appropriately, and inputting J(k) at time intervals that consider the time constant of the physical system (preferably shorter than the time constant of the physical system), interaction between neighboring virtual nodes is strengthened and the high dimensionality and nonlinearity are improved 21,49 .The left-hand and middle panels of Fig. 2a show RC without masking (left) and with masking (middle).When masking is used, time-multiplexing of the input is achieved and high dimensionality is enhanced.While masking generally leads to better computing performance, it creates an extra pre-processing calculation burden.
In the present study, a physical masking was developed and applied to the subject IGR to achieve high performance, as shown in the right-hand panel of Fig. 2a.By utilizing a structural feature of the IGR, multi-input terminals (i.e., gates and drains), a mask waveform can be directly input to the reservoir through the drain electrodes as drain voltage pulse trains, as shown in Fig. 2b.In this case, masking does not require pre-processing of the input and the masking is physically performed.Such is the physical masking we propose in this study.By utilizing a physical mask, the I D response is changed from the one shown in the left-hand panel of Fig. 2b to the one shown in right-hand panel of Fig. 2b.Although the I D response with physical mask seems to appear as a monotonous triangle wave, it does in fact generate reservoir states with excellent diversity.The reservoir states obtained from I D responses (without and with physical masking) shown in Fig. 2b are compared to those in Fig. 2c.Without physical masking, reservoir states are concentrated in a narrow region from 1.92 to 2.17.Conversely, when physical masking is used, reservoir states are spread to six lines, each of which consists of diverse reservoir states.As indicated in the resulting clear differences in the versatility of reservoir states, physical masking significantly contributes to the enhancement of the computing performance of LiCoO 2 redox-IGR, as well as to the inherent Li + trap-free characteristic of LiCoO 2 , as shown in the following section.

Solving a second-order nonlinear dynamic equation
In order to evaluate the effect of the subject physical masking on computational performance, we solved a second-order nonlinear dynamics equation task by a redox-IGR with V D induced physical masking, as shown in Fig. 3a 12,15 .The target waveform y t (k) is generated by the second-order nonlinear dynamic equation shown in Eq. ( 5), which includes second-order nonlinearities and past data: Here, u(k) is a random input ranging from 0 to 0.5.The random input u(k) was converted to a voltage pulse streams with V G of V G (k), a pulse period T of 10 s, duty rate D of 25%, and input to the gate of the IGR.V G (k) was linearly transformed from u(k) to a range of − 1 V to 2 V, as follows, with V G = 0 V at the pulse interval as shown in the upper panel of Fig. 2b: Here, V ap (= 3 V) and V offset (= − 1 V) are the amplitude and offset voltages, respectively.In addition to the drain currents obtained from two channels with different lengths, to achieve higher-dimensional reservoir states via the optimized physical structure, the gate currents with spikes were also used in the reservoir computing, as shown in the lower panel of Fig. 1f.This lead to enhanced high dimensionality due to the variety of reservoir states included 25,26 .These drain currents, corresponding to the reservoir state, were measured with the following two types of drain voltages: (1) V D without physical masking: a constant V D of 0.4 V and (2) V D with physical masking: a stepped triangular wave V D with a voltage range of − 0.4 V to 0.4 V, a period of T/4 for V D1 and − 0.8 V to 0.8 V, and a period of T/2 for V D2 .The I D response with and without physical masking is shown in the lower panel of Fig. 2b.While the I D response exhibits a single relaxation-like behavior without physical masking, with physical masking, it appears as a stepped triangular wave similar to the applied V D stream for physical masking.As will be clarified later, the output with such a triangular wave form includes sufficient variety.To further increase the higher dimensionality of the reservoir states, 20 current values per V G pulse were obtained at virtual nodes, as shown in Fig. 2b.20 reservoir states were obtained from each of the three current responses, so the reservoir size N of the redox-IGR was 60.The reservoir states X i (k) (i = 1,2,…,20) corresponding to I D1 are shown in Fig. 2c.When physical masking is not utilized (i.e., I D responses were measured under constant V D ), the behavior of these reservoir states is similar and low in diversity.On the other hand, when masking (i.e., I D responses were measured with triangular wave V D inputs) is used, the reservoir states are clearly diverse and achieve good high dimensionality.Such high-dimensionality will be discussed later.
The reservoir output is obtained by a linear combination of the readout weights w i which was trained by ridge regression 25 and the reservoir state X i (k) .The computational performance of the redox-IGR in this task was evaluated by 'prediction error' , as follows: (5) y t (k) = 0.4y t (k − 1) + 0.4y t (k − 1)y t (k − 2) + 0.6u 3 (k) + 0.1.
Vol:.( 1234567890  predicted waveform and the target waveform are in better agreement with each other with masking than without physical masking, and Eq. ( 5) is solved more correctly when physical masking is employed.Physical masking also reduced the training error by 65% (prediction error of 6.22 × 10 -4 to 2.16 × 10 -4 ) and the test error by 60% (prediction error of 7.93 × 10 -4 to 3.19 × 10 -4 ).This indicates that V D -induced physical masking is effective in improving the computational performance of redox-IGR.Also, to examine the effects of Physical masking, we performed additional experiments when two signal streams are applied to one gate electrode, and the same single stream is applied to the gate and drain electrodes.We solved a second-order nonlinear dynamics equation task.Applying two signal streams input to a single electrode is a general masking which is the pretreatment of input as shown in Fig. 2a(II) and the prediction error under the condition was 5.38 × 10 −4 which was better than the case without physical masking [prediction error: 7.93 × 10 −4 as shown in Fig. 3b], but worse than the case with physical masking [prediction error: 3.19 × 10 −4 as shown in Fig. 3b].When the same inputs were applied to the gate and drain electrodes, the prediction error was 1.01 × 10 −3 , which was worse than the case without physical masking.Details are explained in the Supplementary Information.According to the results, the physical masking shown as (III) in Fig. 3a was the best among them.Figure 3c shows a comparison of performance with the physical reservoirs that have been reported to date 12,15,25,26 .Without physical masking, the computation performance was slightly lower than with WO 3 redox-IGR, but with physical masking, the computation performance greatly exceeded WO 3 redox-IGR, and the operating speed is also four times faster than that of WO 3 redox-IGR 26 .By masking, the computational performance of the redox-IGR is further improved, making it comparable to that of EDL-IGR, which device exhibits high computational performance 25 .This result proves that masking overcomes the challenges of conventional redox-IGRs in terms of computational performance.The reasons for the significant improvement in computational performance compared with WO 3 redox-IGR will be discussed in later sections.

Solving a NARMA2 task
In addition to the second-order nonlinear dynamic equation, a 2nd-order Nonlinear Auto Regressive Moving Average (NARMA) task was performed, being a task that requires higher computational performance 1,25,26 ; the NARMA2 task is a time series data analysis task, as shown in Eq. ( 8), and is a benchmark commonly used to evaluate the computational performance of RC [24][25][26][50][51][52] : The computational performance of the redox-IGR in this task was evaluated by normalized mean squared error (NMSE) as follows: Here, n is the data length, n = 1100 for the training phase and n = 150 for the test phase.Figure 4a shows the relationship between the NARMA2 score, pulse period T, and duty rate D. The error decreases as D decreases, and is smallest at T = 10 s for all D, with the smallest error NMSE = 0.118 for the condition indicated by the star in the figure (T = 10 s, D = 25%).The target and the predicted output by IGR (test phase) under these conditions are shown in Fig. 4b.If T is too short, the resistance modulation of the LiCoO 2 channel becomes small because the insertion and desertion of Li + (redox) in the channel cannot follow the fast V G pulse change.We considered that this causes the output of the device to become too similar because there is insufficient conduction modulation, which causes a decrease in computational performance.Also, if the T is too long, the next pulse does not input even after complete relaxation of the previous input, resulting in more similar output data, which causes the low performance observed.The neighboring virtual node diversity during the relaxation was particularly reduced.Additionally, it was observed from the color map that calculation performance improves as the duty rate decreases.In contrast, EDL-IGRs show improved calculation performance with increasing duty rate, and an IGR with a duty rate of 75% exhibited the highest performance, which led to results that were different from the previous IGR 25 .The large decrease in score (high NMSE) shown in Fig. 4a, with a duty rate of 100%, is due to the input pulse not reaching 0 V and the relaxation behavior is therefore not included in the output.
Furthermore, in order to improve computational performance within a limited number of nodes, we focused on the correlation between nodes.We reduced the calculation errors by decreasing the correlation between nodes to increase the number of nodes that are effective for computation.To reduce the correlation between the nodes, we changed the drain voltage to from a constant voltage to a triangular wave.A + 0.4 to − 0.4 V triangular wave at a pulse period 4 s was applied to drain electrode 1, which has a short channel length, and a + 0.8 to − 0.8 V triangular wave at a pulse period 10 s was applied to drain electrode 2, which has a longer channel length.As shown in Fig. 4c, the physical masking reduced the error by 72% (NMSE = 0.054) compared to when physical masking was not used.The performance of LiCoO 2 device without physical masking is inferior to the WO 3 device for second-order nonlinear dynamic equation task.In contrast, for NARMA2 task, which is much more difficult than the second-order nonlinear dynamic equation task in general, the performance of LiCoO 2 is far better than the WO 3 device regardless of with or without physical masking.Although the relatively low performance of the LiCoO 2 device was observed for the second-order nonlinear dynamic equation task and we could not clarify the reason, we believe that the performance for the NARMA2 task is more reliable index to discuss the reservoir property.By applying physical masking, redox-IGR achieve computational performance comparable to EDL-IGR, while the physical masking does not require pre-processing to achieve significant improvements in calculation performance.This technique is a highly effective method for improving calculation performance, and can also be applied to other physical reservoirs.

Relationship between the computational performance and memory capacity
We have examined the significant improvement in computational performance from the three perspectives required for reservoirs: short-term memory, nonlinearity, and high-dimensionality 1 .When performing time series data analysis tasks that are dependent on past input, it is necessary for a reservoir to have short-term memory.Short-term memory was evaluated by measuring the memory capacity (MC) of the device through a short-term memory task 1 .Said task examines how well the model can reconstruct past input data as current output.The degree of matching between the target waveform of delay length τ and the output waveform of the trained model can be measured by the coefficient of determination r 2 (τ ) shown in Eq. ( 10) below: (8) Vol.:(0123456789) Here, y τ (k) represents the model output at delay length τ , Cov(•, •) denotes covariance, and Var(•) represents variance, respectively.The possible range of r 2 (τ ) is 0 ≤ r 2 (τ ) ≤ 1 , and if the model can successfully reconstruct the delayed sequence as the model output, r 2 (τ ) takes a value close to 1.The variation of r 2 (τ ) in respect to delay length τ is called the forgetting curve.Forgetting curves with and without physical masking are shown in Fig. 5a.MC is defined as the area under the forgetting curve, which is described as follows: In regions with a long delay length τ , there was almost no change in r 2 (τ ) , but when compared to regions with a short delay length ( τ ≤ 2 ), r 2 (τ ) increased when a physical mask was applied, leading to an increase in MC.Masking is known to improve interactions between virtual nodes, and is accompanied by increasing reservoir size 49 .Because the upper limit of MC is determined by reservoir size, the physical masking in the study increases MC, and this increase in MC led to an increase in the computational performance of the device.
Figure 5b shows the relationship between the computation performance and MC.The downward-sloping relationships between NMSE and MC for both LiCoO 2 and WO 3 redox-IGR, approximated by the two straight lines, evidences that increased MC leads to reduced NMSE, which means improvement in the computational performance of a reservoir 26 .It is also shown that MC increases with the application of physical masking under all experimental conditions, and the NMSE of NAMRA2 is greatly reduced in LiCoO 2 redox-IGR.Although LiCoO 2 redox-IGRs are inferior to WO 3 redox-IGRs in terms of MC, the NMSE is smaller.This deviation from  www.nature.com/scientificreports/ said tendency indicates that the high computational performance achieved in this study is attributed not only to MC, but also from to other requirements (nonlinearity and/or high dimensionality) 1 .

Relationship between computational performance and nonlinearity
Nonlinearity is an element required by a reservoir to enable it to transform non-linear time-series input data, which is not linearly separable into a linearly separable state.Further, strong nonlinearity improves computational performance by diversifying the output and increasing the expressive power of the model 1 .We performed V G sweep measurements in order to investigate the nonlinearity, on-off ratio, and reversibility.Figure 6a compares the normalized I D -normalized V G curves of a LiCoO 2 redox-IGR and a WO 3 redox-IGR 26 .The on-off ratio of I D is larger for the LiCoO 2 redox-IGR than for the WO 3 redox-IGR, which indicates a higher response to V G .Focusing on the normalized I D value at the end of the hysteresis curve, LiCoO 2 redox-IGRs are closer to the initial current value than WO 3 redox-IGRs, which means that LiCoO 2 has better charge-discharge reversibility than WO 3 , and the device behavior is less likely to change even if a pulse voltage is repeatedly applied during calculation.This is quite reasonable if one considers an irreversible Li + trapping into a WO 3 matrix during redox cycles, as has been reported recently [37][38][39] .It further means that the LiCoO 2 redox-IGR has high reproducibility as a time-series input-output converter, and the same time-series output can be obtained for the same time-series input, without depending on random initial conditions.Such good reproducibility in the LiCoO 2 redox-IGR leads to the achievement of the echo state property, which is an important property required for reservoirs, regardless of whether they are simulated or physical reservoirs 2 .
To evaluate nonlinearity, we compared the correlation coefficients of the I D -V G curve and the linear line (I D = − V G ).The correlation coefficient, calculated by Eq. ( 12), is a measure of how linear the I D -V G curve is; if the linearity is high, the correlation coefficient is close to 1, and if the linearity is low, the correlation coefficient is close to 0.
In Eq. (12), n represents the total number of data points, x i and y i are the value of normalized drain current and the value of the linear function, respectively.x, y are the average of each value.Regarding the correlation coefficient with a linear line and an I D -V G curve, the correlation coefficients for the LiCoO 2 redox-IGR and WO 3 redox-IGR are 0.882 and 0.964, respectively, which shows that the LiCoO 2 redox-IGR has a more nonlinear change than the WO 3 redox-IGR (Fig. 6b).Nonlinearity is one of the main functions required of reservoirs in nonlinear transformations of time series input data, and it is known that the higher nonlinearity of systems can increase their computational performance 1 .We attribute the observed performance improvement to the strong nonlinearity of the resistance modulation in the LiCoO 2 redox-IGR, evidenced by the I D -V G curve.
In order to consider the origin of the nonlinearity, we further analyzed the electrical characteristic of the LiCoO 2 redox-IGR.Figure 6c shows variation in x in Li 1−x CoO 2 and hole mobility with respect to V G , which are derived from the I D -V G and I G -V G curves.x showed nonlinear variation in the range from 0.02 to 0.08, which is relatively close to that found in stoichiometric LiCoO 2 .On the other hand, hole mobility is also nonlinearly changed, from 1.8 × 10 -3 to 5.0 × 10 -4 .Near the stoichiometric region, the mechanism of hole transport in LiCoO 2 was reported to be variable-range hopping, which is characteristic of Anderson type insulator-metal transition, and the mobility observed in the present study is consistent with such report 53,54 .The origin of the strong nonlinearity of the LiCoO 2 redox-IGR is attributed to nonlinear changes of both x and hole mobility.

Relationship between computational performance and high dimensionality
In addition to MC and nonlinearity, another important condition required for reservoirs is high dimensionality 1 .High dimensionality facilitates pattern recognition in the readout section by mapping time-series input data to a high-dimensional space.For physical reservoirs, it is important how the number of effective nodes is increased while maintaining low correlation among a limited number of nodes.High dimensionality can be evaluated by the number of effective nodes used in the calculation, which in this case was evaluated by the correlation coefficient r X i , X j between each node, using the following equation, Here, X i and L are the reservoir state of node i and the data length, respectively.The correlation coefficient is a measure of how similar each node is; if the similarity is high, the correlation coefficient is close to 1, and if the similarity is low, the correlation coefficient is close to 0. Figure 7a shows the reservoir state wave form for node 7 (X 7 (red line)) and node 40 (X 40 (black line)), obtained from I D response.The X 7 and X 40 waveform have  almost the same shape, and Fig. 7b shows that they are very strongly correlated, with a correlation coefficient of 0.97.This indicates that the two node states are almost identical, and the reservoirs are not very expressive.On the other hand, the X 45 and X 40 waveforms shown in Fig. 7c are very different, with a low correlation coefficient of 0.32 (Fig. 7d).The large difference in the shape of the node states makes the reservoirs more expressive and reduces the error in the tasks 26 .
Figure 7e−g shows a color map of the correlation coefficients between the nodes of LiCoO 2 redox-IGR and WO 3 redox-IGR 26

Figure 1 .
Figure 1.(a) General scheme of the subject reservoir computing system with (Physical) reservoir.w in and w i denote the input weight and read-out weight, respectively.(b) Schematic image of LiCoO 2 -based redox-iongating reservoir, cross-sectional SEM micrograph of a LiCoO 2 redox-IGR, and insertion (desertion) of Li + in (104) oriented LiCoO 2 .(c) XRD pattern of LiCoO 2 /SrTiO 3 .Stars mark the kβ diffraction peaks.(d) Crosssectional TEM image and electron diffraction of LiCoO 2 /SrTiO 3 .(e) Normalized I D -V G curve of the subject redox-IGR during V G sweeping from 0 to − 4.5 V. (f) Changes in drain (Upper) and gate (Lower) currents when a single pulse of V G is applied.(g) (Upper) V G pulse stream input, (Middle) I D1 and I D2 response, and (Lower) I G response during operation of the redox-ion-gating reservoir. https://doi.org/10.1038/s41598-023-48135-z https://doi.org/10.1038/s41598-023-48135-zwww.nature.com/scientificreports/Here, n is the data length, n = 1100 for the training phase and n = 150 for the test phase.The initial 200 steps were excluded from the computation in order to wash out the initial state of the device.Figure3bshows the predicted and target waveforms obtained without (upper panel) and with (lower panel) physical masks.The (7) prediction error = n k=1 [yt(k)−y(k)] 2 n k=1 [yt(k)] 2 .

Figure 2 .
Figure 2. (a) (I) RC without masking, (II) RC with masking, and (III) RC with physical masking.(b) V G and V D input and I D output w/o and w/ physical masking.(c) Reservoir state waveforms (X 1 , X 2 …, X 20 ) w/o and w/ physical masking.

Figure 3 .
Figure 3. (a) Solving a second-order nonlinear dynamic equation task.(b) Target and prediction waveform of second-order nonlinear dynamics equation task w/o and w/ physical masking.(c) Performance comparison with other physical reservoirs.

Figure 4 .
Figure 4. (a) (Upper) Relationship between NARMA2 score, pulse period T, and duty ratio D in the test phase.(Lower) Diagram of Pulse period and Duty rate D. (b,c) Target and prediction waveforms of the NARMA2 task w/o and w/ physical masking, respectively.(d) NMSEs of the NARMA2 task and reservoir volumes of various physical reservoirs.The reservoir volume of this work was calculated as the total of channel, electrolyte, and electrodes.

Figure 5 .
Figure 5. (a) Forgetting curves w/o and w/ physical masking.(b) Relationship between computational performance and MC.

Figure 6 .
Figure 6.(a) Comparison of normalized I D -normalized V G curve of the LiCoO 2 redox-IGR and WO 3 redox-IGR.(b) Comparison of Nonlinearity in I D -V G curve.(c) x in Li 1-x CoO 2 and hole mobility change of LiCoO 2 in V G sweep.
. The results of WO 3 redox-IGR device are shown as a reference for comparison with the performance of LiCoO 2 redox-IGR in the study26 .In a LiCoO 2 redox-IGR, nodes 1 to 20 correspond to the data obtained from the I D1 , nodes 21 to 40 correspond to the I D2 , and nodes 41 to 60 correspond to the I G .In WO 3

Figure 7 .
Figure 7. (a) X 7 for I D (red line) and X 40 for I D (black line) wave form.(b) Scatter plot between X 7 and X 40 with high correlation (r = 0.97).(c) X 45 for I D (blue line) and X 40 for I D (black line) wave form.(d) Scatter plot between X 45 and X 40 with low correlation (r = 0.32).(e-g) Correlation coefficient heatmap of w/o and w/ physical masking LiCoO 2 redox-IGR and WO 3 redox-IGR.(h) Distribution and average of correlation coefficients.